Array modifier on parent and all of its children
Create your parent object, then create one child. copy the array from the parent to the child Ctrl-L. next take the child and add drivers to all of the parameters in the array modifier that you want to auto update. now copy the drivers and array modifiers onto all  of the other children. Done!

Using drivers is tricky, Here are some tutorials:

https://www.youtube.com/watch?v=o4qYHNA_x4Q

https://www.youtube.com/watch?v=ajMAvKRCTBg

How to copy drivers onto multiple objects